Answer:
Step-by-step explanation:
14. You would add 41 + 41 + 61 + 61 because you just need to add together all the sides.
15. you need to measure the all the sides for 15 and do the same thing that you did on 14
Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
Answer:
D
Step-by-step explanation:
The perimeter P of a rectangle is calculated as
P = 2l + 2w ( l is the length and w the width ) , then
2l + 2(9) = 5364
2l + 18 = 5364 ( subtract 18 from both sides )
2l = 5346 ( divide both sides by 2 )
l = 2673
Then
A = lw = 2673 × 9 = 24057 m² → D
The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference.
Triangle STU is similar to triangle SVW
so
TU ST
------- = ---------- (as you know SV = ST + TV = 12 + 18 = 30)
VW SV
so
TU 12
------- = ----------
40 30
TU = 12 * 40 / 30
TU = 16
answer
16 inches
